Question

Three discs 1, 2 and 3 having radii 2m, 4m and 6m respectively, are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are $Q_1,Q_2$ and $Q_3$ respectively, then which one is true?

• A. $Q_1=Q_2=Q_3$
• B. $Q_1$ is max
• C. $Q_2$ is max
• D. $Q_3$ is max

Answer 1

Answer: (B)

$Q_1$ is max

${\lambda }_1{T}_1={\lambda }_2{T}_2={\lambda }_3{T}_3=$ Constant
$\Rightarrow 3T_1=4T_2=5T_3=K$
As $Q=\sigma A{T}^4$
$=\sigma \pi r^2{T}^4$
$\Rightarrow Q\propto r^2{T}^4$
$\therefore Q_1:Q_2:Q_3=(2{)}^3{\left(\frac{K}{3}\right)}^4:(4{)}^2{\left(\frac{K}{4}\right)}^4:(6{)}^2{\left(\frac{K}{5}\right)}^4$
$=\frac{8K}{81}:\frac{K}{16}:\frac{36K}{625}=\frac{8}{81}:\frac{1}{16}:\frac{36}{625}$
Thus, $Q_1>Q_2>Q_3$